Deconvolution algorithms based on spline interpolation

Convolution preserving spline signals can be deconvolved by using algorithms, which only employ FFT and simple weighting operations with a priori known frequency functions. The method is based on the assumption that the samples of a given signal are interpolated by a spline function of a suitable order. The interpolation must not be executed explicity, it is implicitly performed by certain frequency weighting operations. Solutions are given for spline signals of arbitrary order. Known discontinuities in the given signals, which do not fit well into the respective spline assumptions, can be treated separately. The computational effort is not much higher than that required for deconvolution based on pure DFT.